It's fair to say that four years ago, as FK Sarajevo bobbed around upper mid-table, Mirza Varesanovic, the club's sporting director, was not optimistic. "You can't make progress at the moment," he said. "You can only survive. We are like beggars knocking at the door asking for money. It's hard to do that, because we are a club with a name, with a tradition in Europe."

How things have changed. On Wednesday, Sarajevo face Dynamo Kyiv in the third qualifying round of the Champions League looking to become the first Bosnian side ever to reach the group stages. Given Dynamo have won only one of their opening five games of the Ukrainian season, they have every reason for optimism. The Kosevo Stadium will be rammed to its 36,000 capacity, evoking memories of Safet Susic, Faruk Hadzibegic and Predrag Pasic and the golden age of the early 80s. There probably hasn't been such excitement about a European game for Sarajevo since 1980, when over 50,000 packed in to watch an epic 3-3 draw with Hamburg on their way to a 7-5 aggregate defeat.

What is most remarkable is that Sarajevo have progressed without the benefit of a sugar-daddy. Sarajevo's annual budget remains around £600,000, roughly a thirtieth of that of Genk, the team they beat in the second qualifying round.

The economics have not changed; merely the way of dealing with them. The new sporting director, Mustafa Ducic, has been coldly pragmatic. He picks up players on free transfers, and sells them as soon as he can make a profit without any of the hand-wringing that has accompanied previous departures. The centre-back Vule Trivunovic and the former Under-21 international defender Ajdim Maksumic, for instance, have both gone to the Russian club Khimki this year, while the midfielder Samir Duro joined the Croatian side Medjimurje midway through last season. None of these are big deals, but they are enough.

Three players were signed this summer, all of them on free transfers, all of them on contracts worth 2,000 Bosnian Marks (£700) a month. The 22-year-old midfielder Marko Maksimovoic arrived from Pula in Croatia, Alen Basic moved from Dinamo Dresden, via one game with Kickers Offenbach, and Admir Rascic, once of Sarajevo's great rivals Zeljeznicar, joined from Bela Krajina in Slovenia.

Rascic has taken most of the headlines, scoring twice in the first-round demolition of Marsaxlokk, the Maltese champions, and then, rather more consequentially, pouncing on a defensive error to give Sarajevo the lead away to Genk in the second round. Few are in any doubt, though, that the real hero is the coach, the former Red Star and - briefly - Hearts forward Husref Musemic, who has instilled a discipline and a long-forgotten work ethic. "We saw players running, and that came as a big surprise," as the Bosnian journalist Nedim Hasic commented dryly.

Their progress would be heartening enough, but there is another narrative going on here. Back in the glory days when Sarajevo won two Yugoslav championships, they were an ethnically mixed team, and it would have been bizarre for them to consider being anything else. After the war that changed, and the team became predominantly Bosniak, along with the occasional Bosnian Croat. Over the last couple of years, though, a Serb influence has returned, most notably through the midfielder Vladan Grujic.

Grujic is one of football's great itinerants. He began his career with Borac in his home town of Banja Luka, the major city of the Serb part of Bosnia, and went on to Serbia, Germany, Russia and Bulgaria before joining Sarajevo for 50,000 (£34,000) earlier this year. He was also, more significantly, the first Serb to play for the Bosnia national team, blazing a trail that numerous others have followed. However Grujic himself is blasé about the political significance of his various career choices, insisting everything he has done has been for purely footballing reasons.

Certainly as he and the defender Veldin Muharemovic have vied to be Sarajevo's best player in recent months, nobody much seems to care about his origins. For an outsider, it is hard not be reminded of the point made by the Nobel prize-winning novelist Ivo Andric in The Bridge Over the Drina that what is notable about Balkan history is not its frequent violence, but the periods of cooperation and peace in between.

Football-wise, the long-term prognosis for Sarajevo remains poor. Although qualification for the group stage would provide rewards unprecedented in Bosnian football history, a club cannot continue to prosper spending as much in a year as John Terry earns in a month. On Wednesday night, though, none of that will matter: for Sarajevo, glory, however fleeting it may prove, is within reach once again.